Question 24856
Let number of hours the three machines run be "x" minutes.
Amount of work done by a machine is (rate)(time)
Rate of first machine is 1/12, of second is 1/18, of third is 1/36.
EQUATION:
 Works done by 1st + work done by 2nd P work done by 3rd = 1 job done
       (1/12)x + (1/18)x + (1/36)x = 1 
       3x + 2x + x = 36
              6x = 36
               x = 6 minutes ( time to do job if all machines are running)

Let time run at 7mph by "x" hrs.
The time run at 8mph is "1.5-x" hrs.
Formula:  d=rt
Distance run at 7mph is 7x miles
Distance run at 8mph is 8(1.5-x)= 12-8x miles
EQUATION:
   Dist at 7 + Dist at 8 = 10.9 miles
        7x + 12-8x = 10.9
               -x = -1.1
                x = 1.1 (hrs. at 7mph)
            1.5-x = 0.4 (hrs. at 8mph)
Cheers,
Stan H.